Refined Topological Strings on Local ${\mathbb{P}}^2$

Abstract

We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on ${\mathbb{P}}^2$ (the local ${\mathbb{P}}^2$). The refined topological vertex formalism can not be directly applied to local ${\mathbb{P}}^2$ therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local ${\mathbb{P}}^2$.

16 pages

References in corpus (8)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Extended Holomorphic Anomaly in Gauge Theory
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• M-theory and a Topological String Duality
• Refined Chern-Simons Theory and Topological String
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions
• Mirror of the refined topological vertex from a matrix model

Cited by in corpus (9)

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• Exact quantization conditions for cluster integrable systems
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• Notes on Enhancement of Flavor Symmetry and 5d Superconformal Index
• The refined BPS index from stable pair invariants
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit